Luke Benz

Luke is the creator and maintainer of our NCAA Men’s Basketball Prediction System:


BY THE NUMBERS: Yale Just Falls to LSU: Luke Benz ‘19 breaks down how Yale had a perfect game plan but fell short in March Madness against LSU.

BY THE NUMBERS: Most Exciting Ivy Games: Luke Benz ‘19 uses his Game Excitement Index metric to break down the most exciting basketball games of the Ivy conference slate. 

BY THE NUMBERS: Ivy Hoops Midseason Rankings: Luke Benz ‘19 uses his NCAA Basketball Model to give some Ivy League power rankings at the midpoint of the Ivy season.

BY THE NUMBERS: Ivy Hoops Power Rankings: Luke Benz ‘19 uses his NCAA Basketball Model to give some Ivy League power rankings in advance of conference play hitting full swing.

Game Excitement Index: An In-Depth Exploration: Luke Benz ‘19 takes a deep dive into his Game Excitement Index metric to deterimine which NCAA Men’s Basketball games, teams, and conferences have been the most exciting this season.

Weighting Schema for Regression Based Ratings and Prediction in Australian Rules Football: Luke Benz ‘19 examines how various weighting functions for weighted least squares regression impact prediction of Aussie Rules Football games.

A Bayesian Examination of Win Probability and Timeout Usage in NCAA Men’s Basketball: Luke Benz ‘19 presents a Bayesian win probability model for college basketball as part of a final project for BIS 567: Bayesian Statistics.

BY THE NUMBERS: Yale vs. Duke Preview: Krish Maypole ‘21 and Luke Benz ‘19 preview the upcoming Yale vs. Duke men’s basketball clash and analyze strengths and weaknesses of the two squads. 

BY THE NUMBERS: Yale vs. Duke Preview: Krish Maypole and Luke Benz preview the upcoming Yale vs. Duke men’s basketball clash and analyze strengths and weaknesses of the two squads. 

BY THE NUMBERS: A Statistical History of The Game: Luke Benz ‘19 examines a the history of the Harvard-Yale football game since 1875.

BY THE NUMBERS: Princeton’s Success: Krish Maypole ‘21 and Luke Benz ‘19 place Princeton’s historically dominant football season in context and offer some keys to the Yale-Princeton football game.

NCAA Hoops Methodology Update: Luke Benz ‘19 debuts a new methodology for NCAA Hoops rankings, included player adjusted preseason priors.

BY THE NUMBERS: Rise of Ivy League Football Recruiting: Using data from 247Sports, Luke Benz ‘19 examines the recent rise in recruiting success in Ivy League football.

BY THE NUMBERS: Ivy League Football Preview: Luke Benz ‘19 gives a 2018 Ivy League Football preview based simulations using the YUSAG FCS model.

Summer 2018

ncaahoopR: Luke Benz ‘19 introduces ncaahoopR, an R package for working with NCAA Men’s Basketball Play-by-Play data.

You Play to … Lose the Game: Luke Benz ‘19 takes a stab at answering the question of whether England or Belgium shoud try and lose their final match in hopes of receiving a better draw in the Knockout Rounds of the World Cup.

World Cup Probability Quirks: Luke Benz ‘19 notes somes neat probability paradoxes in World Cup odds prior to matchday 3.

World Cup Model Methodology: Luke Benz ‘19 and Dan Tokarz ‘20 dive into the math underlying their World Cup poisson model in advance of the 2018 FIFA World Cup.


BY THE NUMBERS: Baseball MVPs: Luke Benz ‘19 turns to Ivy League Baseball Wins Above Replacement to identify the most valuable players in the Ancient Eight.

BY THE NUMBERS: Softball MVPs: Luke Benz ‘19 turns to Ivy League Softball Wins Above Replacement to identify the most valuable players in the Ancient Eight.

538 Riddler: Transitive National Champions: Luke Benz ‘19 uses graph theory to show that all 351 Division 1 teams are transitive national champions in the solution to this week’s FiveThirtyEight riddler.

BY THE NUMBERS: How Mad was March?: Luke Benz ‘19 creates a new metric comparing each year’s NCAA basketball tournament to the average tournament in order to contextualize just how crazy the 2018 tournament was.

Ivy League Baseball Softball WAR 2018: Luke Benz ‘19 updates the Ivy League WAR database for 2018.

Do Deep NIT Runs Predict Future NCAA Success: Luke Benz ‘19 takes a dive into KenPom adjEM to see if deep NIT runs predict future NCAA success.

Game Excitement Index Part II: Luke Benz ‘19 uses in game win probability charts to derive a new in-game game excitement index metric.

BY THE NUMBERS: Yale Heads to Ivy Madness: Luke Benz ‘19 previews the 2nd iteration of the Ivy League Men’s and Women’s Basketball Tournament with title odds and breakdowns of potential championship matchups.

BY THE NUMBERS: Ivy Hoops Enters Home Stretch: With four games left in Ancient Eight Confernce Play, Luke Benz ‘19 details each’s teams math to the Palestra.

BY THE NUMBERS: Math to Ivy Madness: Luke Benz ‘19 hits reset on the Ivy League as conference play enters the seconf half of the season.

BY THE NUMBERS: Ivy Basketball Analytics: Luke Benz ‘19 assess each Ivy League’s team’s chances of reaching Ivy Madness and explains why this weekend’s games against Harvard and Dartmouth are especially important.

Mid-Season Assist Network Report: Luke Benz ‘19 creates “All-American Assist Teams” using various centrality metrics from his assist network charts.

Improving College Basketball Win Probability Model: Luke Benz ‘19 turns to Bart Torvik and Ken Pomeroy to improve his in-game college basketball win probability model minimum win probability estimates for late game scenarios.

NCAA Basketball Assist Network App: Luke Benz ‘19 rolls out an R Shiny App of his college basketball assist networks.

College Basketball Conference Title Favorites: On the dawn of conference play, Luke Benz ‘19 compiles a list of favorites to win each NCAA conference’s regular season tournament.

Union Street Hoops Podcast: Luke Benz ‘19 joins Paul Oren of the Northwest Indiana Times to discuss his recent article, “The Value of Switching Conferences”, previews the beginning of Missouri Valley Conference play, and explores Valparaiso’s long-term outlook in the MVC.

The Value of Switching Conferences: Luke Benz ‘19 quantifies how changing conferences has effected the men’s basketball teams from Wichita St., IUPUI, and Valparaiso.

BY THE NUMBERS: Replacing Makai Mason: Luke Benz ‘19 debuts college basketball assist networks to examine how Yale’s offense has done without its star point guard.

NCAA Basketball Win Probability Model: Luke Benz ‘19 breaks down the methodology for his newly developed in-game win-probability model for college basketball.

BY THE NUMBERS: Ivy Title Race Heats Up: Luke Benz ‘19 and Matt Robinson ‘18 break down the numbers you need to know for the final 3 weeks of the Ivy League Football season.

BY THE NUMBERS: Ivy League Football Quick Hits: Luke Benz ‘19 examines title odds and Yale’s outlook at the midway point of the football season.

BY THE NUMBERS: How to Win an Ivy League Football Championship: Luke Benz ‘19 breaks down why controlling the running game is much more important than controlling the passing game for winning titles in the Ivy League.

Summer 2017

Ivy League TiebreakR: Luke Benz ‘19 debuts an R Shiny App for breaking Ivy League basketball ties for any desired season permuation.

Bracket Math: The YUSAG Database for all metrics used in YUSAG Bracketology. (By: Luke Benz ‘19) 

YUSAG Bracketology: Luke Benz ‘19 debuts YUSAG Bracketology predictions for the NCAA Men’s Basketball Tournament.

NCAA Basketball Game Excitement Index: Luke Benz ‘19 introduces an new metric for predicting game excitement in order to help choose the best game(s) to watch on a limited time schedule. 

NCAA Basketball Model Methodology: Luke Benz ‘19 breaks down the inner workings of his NCAA hoops prediction model, and shares many new features for the 2017 season.

Effect of Base Runners on MLB Pitch Selection:Michael Bogaty ‘19, Tyler Duncan ‘18, and Luke Benz ‘19 examine how having runners on baser–particularly base stealing threats–influences pitch selection in MLB.

NCAA Baseball Model Methodology: A little post about the workings of our NCAA Baseball Model.

Yale Baseball Postseason Predictions: Luke Benz ‘19 simulates the NCAA Baseball tournament to determine Yale’s chances for postseason success.

All-Ivy Baseball/Softball Snubs and Surprises: Luke Benz ‘19 uses his WAR project to evaluate the Ivy League’s all-conference honors and doles out some hot takes.

What Makes a Cy Young?: Luke Benz ‘19 examines whether dominance or consistency is more important in order to be named a Cy Young Award winner.


BY THE NUMEBRS: Baseball/Softball MVPs: Luke Benz ‘19 analyzes the most valuable Ivy League Baseball/Softball players using Wins Above Replacement (WAR) and other advanced MLB stats.

Ivy League Baseball/Softball WAR: Luke Benz ‘19 brings Wins Above Replacement (WAR) and other advanced MLB stats to Ivy League Baseball and Softball.

BY THE NUMBERS: Ivy League Lacrosse Predictions: Daniel Tokarz ’20 and Luke Benz ‘19 break down the odds for the Yale Men’s and Women’s Lacrosse teams to reach the postseason.

NCAA Basketball Championship Difficulties: Luke Benz ‘19 creates a new metric as a way to measure which NCAA Basketball champions had the most difficult run to the title, and says to stop hating on Gonzaga.

BY THE NUMBERS: Ivy Math-ness: Luke Benz ‘19 previews the Ivy League basketball tournament, assigning odds to each team’s chances of reaching March Madness. Benz also breaks down what must go right for the Bulldogs if they wish to beat rival Harvard.

BY THE NUMBERS: Math To The Palestra: Luke Benz ‘19 and Michael Bogaty ’19 break down odds and scenarios for the Yale Men’s and Women’s Basketball teams for make the Ivy League tournament.

On The Vine: Luke Benz ‘19 joins the Ivy Hoops Online weekly podcast, On the Vine, to discuss Ivy League Basketball and #MathToThePalestra

BY THE NUMBERS: Hoops Analysis: Luke Benz ‘19 and Michael Bogaty ’19 examine updated playoff odd for the inaugural Ivy League Tournament after the first full weekend of Ancient Eight play.

BY THE NUMBERS: Ivy Hoops Games to Watch: Luke Benz ‘19 introduces the “Playoff Swing Factor” to Ivy League Basketball and analyzes which games will have the biggest impact on the playoff race.

BY THE NUMBERS: Ivy Hoops Weekend Recap: We help the Yale Daily News kick off their new sports blog, “Down the Field”, with an analytical recap of last weekend’s Ivy League Men’s Basketball games.

BY THE NUMBERS: Basketball Begins: Continuing our collaboration with the Yale Daily News, Luke Benz ‘19 previews the Ivy League Men’s Basketball season and explores team’s chances of reaching the Ivy League Tournament in March.

CS50: What I Learned: Luke Benz ‘19 discusses his NBA related final project for CS50 and shares the analytical observations he made along the way.

Total Defensive Pressure (TDP): Analysis of Off Ball Defense in the NBA: In the inaugural NBA Hackathon, we took the opportunity to analyze SportsVU tracking data and create a new metric for off ball defense which had mostly been neglected by the current  research. The metric was based on the sum of squared distances from each offensive player to the defender closer to him. We found that closer off ball defense was related to more missed shots and fewer three points attempts. We also noted individual differences in effort based on differences in on ball and off ball defense.


Player Clustering in the NBA: As a result of position, physical attributes, or basketball ability players in the NBA naturally gravitate toward certain roles within a team. We attempt to formalize this notion by clustering NBA players based on a combination of traditional and advanced statistics. These clusters can then be applied to examine how teams construct lineups.